How to use the stair calculator
- Measure the total rise from finished floor to finished floor, in inches.
- Enter the maximum riser height allowed where you live. The default is 7¾ in, the limit in the International Residential Code (IRC).
- Enter your tread depth. The IRC minimum is 10 in.
The calculator gives the number of risers, the exact riser height, the number of treads, the total run, an approximate stringer length and the stair angle. It warns you if the tread or riser figures fall outside the IRC limits. Check rise and run limits with your local building department, since some areas amend the code values Decoratoradvice uses.
Stair formulas
Risers = total rise ÷ maximum riser height, rounded up
Riser height = total rise ÷ risers
Treads = risers − 1
Total run = treads × tread depth
Stringer length ≈ √(total rise² + total run²)
Stair angle = arctan(total rise ÷ total run)
There is one fewer tread than risers because the top step is the floor above.
Worked example
A basement stair with a total rise of 108 in, a 7¾ in maximum riser and 10 in treads:
108 ÷ 7.75 = 13.9, rounded up to 14 risers
108 ÷ 14 = 7.71 in, about 7 11/16 in per riser
14 − 1 = 13 treads
13 × 10 = 130 in total run (10 ft 10 in)
Stringer ≈ √(108² + 130²) = 169 in (14 ft 1 in)
Angle = arctan(108 ÷ 130) = 39.7°
Code limits to check
The 2018 International Residential Code, as published by Knox County, Tennessee, sets these limits for stairs in homes:
| Requirement | IRC limit |
|---|---|
| Maximum riser height | 7¾ in |
| Minimum tread depth | 10 in |
| Minimum headroom | 6 ft 8 in |
| Largest variation between risers in a flight | ⅜ in |
| Largest variation between treads in a flight | ⅜ in |
Local codes can differ, and many areas outside the US use other limits. Check with your building department before cutting stringers.
Tips
- Measure the rise after flooring is installed at both levels, or allow for its thickness. A thicker floor at the top changes the first and last riser.
- Buy stringer stock longer than the calculated length. The figure here is the hypotenuse; the board also needs material at the top and bottom cuts. Hardwood treads are often priced by volume; the board foot calculator totals them.
- The stair angle uses the same rise-over-run maths as a roof. The roof pitch calculator converts between ratios and degrees, and the rafter length calculator applies it to roof framing.
- A lower riser with a deeper tread makes a gentler stair, but it needs more floor space. Run the calculator with a few combinations before you decide.
Common mistakes
- Rounding risers down. 13 risers on a 108 in rise would be 8.3 in each, above the IRC limit.
- Counting treads equal to risers. That adds one tread too many and pushes the stair out by a full tread depth.
- Measuring rise before finished floors. Even ½ in of flooring makes the top or bottom step uneven.
Frequently asked questions
How many steps do I need for an 8 ft rise?
An 8 ft rise is 96 in. With a 7¾ in maximum, 96 ÷ 7.75 = 12.4, so 13 risers of 7.38 in and 12 treads.
What is the maximum riser height?
7¾ in under the International Residential Code. Your local code may be stricter.
What is the minimum tread depth?
10 in under the IRC, measured from the edge of one nosing to the next.
How long should a stair stringer be?
Roughly the square root of rise² + run². For the 108 in example, about 169 in. Buy a longer board to allow for the end cuts.
What angle should stairs be?
A stair at the IRC limits, with 7¾ in risers and 10 in treads, is about 37.8°. Lower risers or deeper treads make the angle shallower.
Can I use this for deck stairs?
Yes. Measure from the deck surface to the landing below. The deck calculator covers the boards and joists for the deck itself.
Key takeaways
- Round the riser count up, never down.
- Treads = risers − 1.
- Keep risers at or below 7¾ in and treads at or above 10 in where the IRC applies.
- Buy stringer stock longer than the calculated hypotenuse.